Introduction to Game Theory

Game Theory might be better described as Strategy Theory, or Theory of Interactive Decision Making. A strategic situation involves two or more interacting players who make decisions while trying to anticipate the actions and reactions by others. Game theory studies the general principles that explain how people and organizations act in strategic situations.

Game theory studies strategy mainly through the analysis of different "games". A "game" in game theory is a fully explicit structure which characterizes each player's set of actions, payoffs and possible outcomes under given rules of playing. Given this conditions, rational players act in such a way, that they maximize the expected value of their von Neumann-Morgenstern Utility. Games provide a simplified world within which to study strategy (as opposed to the real world where complexities get in the way of developing general principles).

Table of Contents

1 Introduction to Game Theory

1. Overview
2. Short history
3. Theory of rational choice

Part I - Games with Perfect Information

2 Nash Equilibrium

1. Strategic games
2. Example: Prisoner's Dilemma
3. Matrix Notation In Game Theory - How To Set Out A Game
4. Example: Battle of the sexes (a.k.a. Bach or Stravinsky?)
5. Example: Matching Pennies
6. Nash equilibrium
7. Best response functions
8. Cournot's model of oligopoly
9. Bertrand's model of oligopoly
10. Auctions
11. Questions
12. Sources

3 Mixed Strategy Equilibrium

1. Randomization
2. Mixed strategy Nash equilibrium
3. Dominated actions
4. Dominant Strategies
5. Example: expert diagnosis
6. Formation of beliefs

4 Extensive Games with Perfect Equilibrium

1. Introduction to Extensive games
2. Strategies and outcomes
3. Nash equilibrium
4. Subgame perfect equilibrium
5. Stackelberg's model of duopoly
6. Adding simultaneous moves
7. Adding uncertainty

5 Coalitional Games

Part II - Games with Imperfect Information

6 Bayesian Games

1. Motivational Examples
2. Cournot's duopoly with imperfect information

7 Extensive Games with Imperfect Information

1. Strategies
2. Nash equilibrium
3. Beliefs
4. Signaling games

Part III - Real World Examples

8 TV Game Shows

1. Deal Or No Deal

9 Politics

1. Mutually assured destruction

See Also

Wikipedia Articles on Game Theory Related Topics

• Game Theory article on Wikipedia
• Prisoner's Dilemma.
• John von Neumann and John Forbes Nash.
• Game semantics, an approach to establish the notion of truth in mathematical logic, in another way than Tarski did, using game theoretical concepts